A few newbie questions about 14-45mm vs 20mm

My 14-45mm (that I got from Bokeh Diem) has arrived, so I am going to go play around with it some time.

There are just a few things that have been bugging me:

1) Is there a correlation between minimum focal distance and focal length (as in like 14-45mm vs 20mm)?
As I understand the focal length determines the field of view and the min focal distance relates to the lens design itself.

2) How does the 14-45mm perform in low light with OIS compared with the 20mm? i.e. assuming DOF is not important, would I get "better" image at 14mm f/3.5 with a slower shutter speed (say 1/8s) compared to 20mm at say f/2.0 at 1/20s? Also is there any impact on image quality with OIS (why is there an on/off switch, I mean IS is always good right)?)
The reason I ask this is usually I avoid turning up ISO, but I have trouble keeping a steady hand at SS slower than 1/20s to 1/10s with the 20mm.

well is takes power, and in daytime outdoor at 1\500 or 1\1000 it draining the batts for nothing , further ois is good to a poin,t for slow shutter speeds its a godsend allowing sharp exposures at slower speeds at certain points in a shutter speed range for a given focal lgnth . otherwise impossible .... but which situiations ??

practice shooting in low roomlite moving subj other people or pets .... nonmoving subj slower speeds too...
the 20 is a great advantage in low light, the zoom can give you more or less reach instantly in brighter conditions .... shoot and review , and all will soon be clear
shooting conditions are so variable there is no one right answer, both are useful but the 20 is your low light friend

example ....i just compared my 17 2.8 oly pancake vs 14-45 panny kit zoom shooting in low roomliight on my gf1..how well?
a test for image stab. effectiveness at 1\6 sec........
first the kit pancake [ no ois!] at 1\6 ...5 shots taken of a stack of books about 2 meters away in review they mostly look ok but in magnified review the titles on the spines are blurred in all, some of the small print completely illegible
now the kit zoom ... at just below the 18 mark ... also 1\6sec .... 5 shots
enlarged... the writing on the book spines is sharp even tiny print ,thus , ois is working well in this instance , in another instance perhaps 1\2 a sec ,it might not save matters , lots of practice situations like this help me understand what my lenses can do and what they cant , i am teaching myself evey day ,
shooting and reviewing is the best way to kill 30 minutes you might otherwise devote to suduko ,
anyway that what i like to do..... cheers

1. Focal length and minimum focus distance are not related. It's a design issue. But the natuaral increase in DOF offered by wide lenses will allow them some close focusing advantages.

2.image stabilisation is good for accomodating for camera shake, which we all have. The switch is there so you can turn it off when using high shutter speeds and when using a tripod. It will also save battery power.

image stabilisation will not help freeze subject movement. So if you shoot moving subjects you're better off with a highr shutter speed. If your subjects are stationary then you will benifit from OIS (or equiv) more. OIS generally will not impact on image quality unless you leave it on while using a tripod or at higher shutter speeds (apparently this is acknowledged on m4/3 cameras and has been discussed recently on this site).

With regard to your first question, minimum focus distance is determined by the design of the lens, and doesn't change as the focal length of the lens changes. So you'll always get the most magnification at the long end of the zoom range on a zoom lens.

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